Physical systems, such as an electrical utility system or a heating, ventilation, and air conditioning (HVAC) system, may be monitored by a network of intelligent electronic devices (“IEDs”) coupled to a computer and/or server for monitoring various parameters or characteristics of the physical system. In addition to monitoring these systems, the physical systems may be modeled mathematically in a number of ways. Generally, the models take one or more observable qualities of the physical system that can be measured or observed and predict a numerical characterization of some other quality of the system that is thought to be causally influenced by the observed qualities. The observable qualities of the physical system that can be measured or observed are referred to as “driver variables,” or “independent variables.” The quality of the system that is thought to be causally influenced by the driver variables is called the “modeled variable,” or “dependent variable.” One approach to modeling a physical system is by the use of a linear model built using regression analysis on historical data from the system (hereinafter “regression model”), which computes a predicted quantity as a linear combination of scaled input quantities.
Energy consumption may be a cost driver in these types of physical systems. A producer of goods that is able to monitor its energy consumption, and thus its energy costs, is able to take steps to manage its energy consumption by making adjustments to its energy consumption (e.g., by modifying its physical installation to more efficiently consume energy with new windows, insulation, door seals, and the like, by adjusting working days to require less heating/cooling, etc.). Effective modeling can also provide verification that a proposed change in practices or equipment that influences energy consumption (e.g., modification to physical installation) has achieved the change in energy consumption desired. In addition, effective modeling can provide guidance on cost effectiveness of particular changes in energy consumption in order to target a producer's energy consumption management toward the most effective proposed changes. Thus, the more efficiently a producer of goods (or any other energy consumer) is able to monitor its energy consumption, the more efficiently the producer is able to manage energy consumption and energy costs, and thereby achieve a lower overall cost of producing the good.
Linear models can be used to model energy consumption as a function of one or more independent variables (driver variables). A simple linear model for a single independent variable has the form: y=mx+b, for example. A linear model with multiple independent variables can have the form: y=m1x+m2z+ . . . +b. Furthermore models of energy consumption patterns can be generated using a piecewise linear model, such as a changepoint model, in order to roughly account for non-linear behavior in an energy consumption pattern with respect to the driver variables.